/// [Maximum path sum I](https://projecteuler.net/problem=18)
fn main() {
    for triangle in &[
        "3
        7 4
        2 4 6
        8 5 9 3",
        "75
        95 64
        17 47 82
        18 35 87 10
        20 04 82 47 65
        19 01 23 75 03 34
        88 02 77 73 07 63 67
        99 65 04 28 06 16 70 92
        41 41 26 56 83 40 80 70 33
        41 48 72 33 47 32 37 16 94 29
        53 71 44 65 25 43 91 52 97 51 14
        70 11 33 28 77 73 17 78 39 68 17 57
        91 71 52 38 17 14 91 43 58 50 27 29 48
        63 66 04 68 89 53 67 30 73 16 69 87 40 31
        04 62 98 27 23 09 70 98 73 93 38 53 60 04 23",
    ] {
        let rst = maximum_path_sum_i(*triangle);
        let rst_str: Vec<String> = rst.iter().map(|n| n.to_string()).collect();
        println!("{} = {}", rst_str.join(" + "), rst.iter().sum::<u64>());
    }
}
fn maximum_path_sum_i(triangle_str: &str) -> Vec<u64> {
    let mut triangle: Vec<Vec<u64>> = vec![];
    for line in triangle_str.lines() {
        triangle.push(line.split_whitespace().map(|x| x.parse().unwrap()).collect());
    }
    let mut index: Vec<Vec<usize>> = vec![vec![0; triangle[triangle.len() - 1].len()]; triangle.len() - 1];
    let mut value: Vec<u64> = triangle[triangle.len() - 1].clone();
    for i in 2..=triangle.len() {
        let mut tmp: Vec<u64> = vec![];
        let j = triangle.len() - i;
        for k in 0..=j {
            if value[k] >= value[k + 1] {
                index[j][k] = k;
                tmp.push(triangle[j][k] + value[k])
            } else {
                index[j][k] = k + 1;
                tmp.push(triangle[j][k] + value[k + 1])
            }
        }
        value = tmp;
    }
    let mut j = 0;
    let mut list: Vec<u64> = vec![triangle[0][0]];
    for i in 0..index.len() {
        j = index[i][j];
        list.push(triangle[i + 1][j]);
    }
    list
}
